robustness winsolized mean

*The author of this computation has been verified*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Tue, 20 Oct 2009 09:50:38 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053909umgj0hx3hm0rzgo.htm/, Retrieved Tue, 20 Oct 2009 17:51:52 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053909umgj0hx3hm0rzgo.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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9.738444444 9.738444444 9.548444444 9.378444444 10.04844444 13.17844444 13.14844444 12.75844444 12.00844444 11.39844444 10.86844444 10.27844444 9.528444444 9.278444444 8.858444444 8.478444444 8.118444444 7.778444444 7.458444444 7.128444444 6.398444444 5.288444444 4.408444444 3.648444444 2.938444444 1.318444444 -8.071555556 -8.771555556 -7.481555556 -3.591555556 -1.741555556 0.248444444 4.028444444 5.528444444 6.798444444 7.558444444 7.708444444 6.718444444 6.088444444 8.898444444 7.758444444 6.558444444 5.818444444 4.938444444 4.038444444 2.928444444 1.798444444 4.588444444 4.148444444 3.158444444 2.338444444 1.618444444 0.838444444 -0.121555556 -1.071555556 -2.081555556 -3.061555556 0.728444444 3.158444444 2.368444444 1.208444444 0.238444444 3.598444444 3.538444444 2.488444444 1.368444444 0.468444444 -0.641555556 -1.571555556 4.388444444 2.728444444 1.128444444 -0.121555556 -1.381555556 -2.841555556 -1.151555556 -1.501555556 -2.8915 etc...

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -0.00338889132222219 0.993560981023654 -0.00341085387504917 Geometric Mean NaN Harmonic Mean -5.36200305405527 Quadratic Mean 18.8252936324016 Winsorized Mean ( 1 / 120 ) -2.43333329782066e-09 0.993194541447273 -2.45000671698702e-09 Winsorized Mean ( 2 / 120 ) -0.078777780211111 0.973042432547363 -0.0809602722102014 Winsorized Mean ( 3 / 120 ) -0.161194446877778 0.955044856654519 -0.168782068983058 Winsorized Mean ( 4 / 120 ) -0.322861113544444 0.924609648063579 -0.34918639906107 Winsorized Mean ( 5 / 120 ) -0.414111113544444 0.909725896872654 -0.455204270833694 Winsorized Mean ( 6 / 120 ) -0.433111113544444 0.905989502543606 -0.478053125702302 Winsorized Mean ( 7 / 120 ) -0.499027780211111 0.896283439213933 -0.556774518392053 Winsorized Mean ( 8 / 120 ) -0.564138891322222 0.885616688034374 -0.63700119808529 Winsorized Mean ( 9 / 120 ) -0.561138891322222 0.884119772364234 -0.634686508392042 Winsorized Mean ( 10 / 120 ) -0.619194446877778 0.876301225037233 -0.706600001445245 Winsorized Mean ( 11 / 120 ) -0.678472224655556 0.868738956468808 -0.780985150491425 Winsorized Mean ( 12 / 120 ) -0.707472224655555 0.863359864773918 -0.81944071472539 Winsorized Mean ( 13 / 120 ) -0.716500002433333 0.86218105581837 -0.831031948101947 Winsorized Mean ( 14 / 120 ) -0.735555557988889 0.858033680560572 -0.857257208724411 Winsorized Mean ( 15 / 120 ) -0.762222224655556 0.853804611046615 -0.892736130484473 Winsorized Mean ( 16 / 120 ) -0.7946666691 0.849553612814746 -0.93539319604222 Winsorized Mean ( 17 / 120 ) -0.783805557988889 0.84779738137531 -0.92451990912898 Winsorized Mean ( 18 / 120 ) -0.863805557988889 0.838736421212793 -1.02988917154670 Winsorized Mean ( 19 / 120 ) -0.8706666691 0.836272071387618 -1.04112847826582 Winsorized Mean ( 20 / 120 ) -0.899555557988889 0.832342300040764 -1.08075194297446 Winsorized Mean ( 21 / 120 ) -0.897805557988889 0.831729941412618 -1.07944359495349 Winsorized Mean ( 22 / 120 ) -0.949750002433333 0.82451682073879 -1.15188675178552 Winsorized Mean ( 23 / 120 ) -0.960611113544444 0.816656487536445 -1.1762731677333 Winsorized Mean ( 24 / 120 ) -0.971944446877778 0.81555133105935 -1.19176366938827 Winsorized Mean ( 25 / 120 ) -0.992083335766666 0.813077536573607 -1.22015833809332 Winsorized Mean ( 26 / 120 ) -1.01230555798889 0.811131884605754 -1.24801598507117 Winsorized Mean ( 27 / 120 ) -1.08880555798889 0.797668598653516 -1.36498485690275 Winsorized Mean ( 28 / 120 ) -1.1199166691 0.79394943781211 -1.41056421953791 Winsorized Mean ( 29 / 120 ) -1.11508333576667 0.788824579438917 -1.41360115395975 Winsorized Mean ( 30 / 120 ) -1.04925000243333 0.782650864264009 -1.34063610013391 Winsorized Mean ( 31 / 120 ) -1.03719444687778 0.776507878326423 -1.33571657909409 Winsorized Mean ( 32 / 120 ) -1.11630555798889 0.757250506819193 -1.47415623751497 Winsorized Mean ( 33 / 120 ) -1.14197222465556 0.754857678519454 -1.51283116957275 Winsorized Mean ( 34 / 120 ) -1.1259166691 0.751678434784057 -1.49787012237946 Winsorized Mean ( 35 / 120 ) -1.1696666691 0.746746624278461 -1.56635012609556 Winsorized Mean ( 36 / 120 ) -1.1746666691 0.746148739310498 -1.57430631081075 Winsorized Mean ( 37 / 120 ) -1.27230555798889 0.73723916537721 -1.72577043887503 Winsorized Mean ( 38 / 120 ) -1.27125000243333 0.732865862801423 -1.73462848654719 Winsorized Mean ( 39 / 120 ) -1.32433333576667 0.725254082118562 -1.8260267241766 Winsorized Mean ( 40 / 120 ) -1.3776666691 0.719305581540697 -1.91527315296114 Winsorized Mean ( 41 / 120 ) -1.38222222465556 0.710294828750198 -1.94598379251564 Winsorized Mean ( 42 / 120 ) -1.42188889132222 0.699205935089438 -2.03357669030705 Winsorized Mean ( 43 / 120 ) -1.40158333576667 0.694585948763018 -2.01786883000258 Winsorized Mean ( 44 / 120 ) -1.45169444687778 0.68781729964576 -2.11058146927306 Winsorized Mean ( 45 / 120 ) -1.45169444687778 0.68163474427296 -2.12972484028257 Winsorized Mean ( 46 / 120 ) -1.44530555798889 0.680489556964874 -2.12392026181159 Winsorized Mean ( 47 / 120 ) -1.43225000243333 0.678982503633193 -2.10940634665761 Winsorized Mean ( 48 / 120 ) -1.4549166691 0.675599264205325 -2.15352020966356 Winsorized Mean ( 49 / 120 ) -1.51480555798889 0.670529501197778 -2.25911843592708 Winsorized Mean ( 50 / 120 ) -1.55369444687778 0.66638641193477 -2.33152180034227 Winsorized Mean ( 51 / 120 ) -1.53386111354444 0.661630003666328 -2.31830646289433 Winsorized Mean ( 52 / 120 ) -1.46019444687778 0.654403588233693 -2.23133624743563 Winsorized Mean ( 53 / 120 ) -1.41308333576667 0.649633617320356 -2.17520044851655 Winsorized Mean ( 54 / 120 ) -1.51958333576667 0.626919391974283 -2.42388950672147 Winsorized Mean ( 55 / 120 ) -1.53638889132222 0.625748110558373 -2.45528330872827 Winsorized Mean ( 56 / 120 ) -1.48038889132222 0.619123056397015 -2.39110605884611 Winsorized Mean ( 57 / 120 ) -1.45347222465556 0.616256688102505 -2.35855002098378 Winsorized Mean ( 58 / 120 ) -1.43252778021111 0.614586949295824 -2.33087894536723 Winsorized Mean ( 59 / 120 ) -1.4341666691 0.613493788227685 -2.33770365180575 Winsorized Mean ( 60 / 120 ) -1.5491666691 0.604343645822988 -2.56338703948870 Winsorized Mean ( 61 / 120 ) -1.53052778021111 0.602104334432711 -2.54196439501327 Winsorized Mean ( 62 / 120 ) -1.54086111354444 0.596838805153846 -2.58170397138849 Winsorized Mean ( 63 / 120 ) -1.52161111354444 0.595053027770828 -2.55710170780017 Winsorized Mean ( 64 / 120 ) -1.53050000243333 0.592108264991997 -2.58483134406850 Winsorized Mean ( 65 / 120 ) -1.3246666691 0.575772991903154 -2.30067524480692 Winsorized Mean ( 66 / 120 ) -1.35583333576667 0.569949114660177 -2.37886734252594 Winsorized Mean ( 67 / 120 ) -1.32233333576667 0.566844583901760 -2.33279698407746 Winsorized Mean ( 68 / 120 ) -1.34688889132222 0.557609135246634 -2.41547135114005 Winsorized Mean ( 69 / 120 ) -1.26063889132222 0.551076628356668 -2.28759273475541 Winsorized Mean ( 70 / 120 ) -1.19647222465556 0.542686868686689 -2.20471932101662 Winsorized Mean ( 71 / 120 ) -1.21027778021111 0.541761563104635 -2.23396760241804 Winsorized Mean ( 72 / 120 ) -1.22227778021111 0.540394145665032 -2.26182646502753 Winsorized Mean ( 73 / 120 ) -1.19388889132222 0.528876227270543 -2.25740698817891 Winsorized Mean ( 74 / 120 ) -1.2966666691 0.521265827098496 -2.48753438589595 Winsorized Mean ( 75 / 120 ) -1.26125000243333 0.518646047210411 -2.43181261906283 Winsorized Mean ( 76 / 120 ) -1.13669444687778 0.507780550886584 -2.23855451905968 Winsorized Mean ( 77 / 120 ) -1.12172222465556 0.50110253396836 -2.23850838624253 Winsorized Mean ( 78 / 120 ) -0.879055557988889 0.4800849309681 -1.83104176216541 Winsorized Mean ( 79 / 120 ) -0.905388891322222 0.478352125579707 -1.89272471659867 Winsorized Mean ( 80 / 120 ) -0.898722224655556 0.475489264965695 -1.89009992627362 Winsorized Mean ( 81 / 120 ) -0.810972224655556 0.469143696148238 -1.72862223517826 Winsorized Mean ( 82 / 120 ) -0.842861113544444 0.4643052860977 -1.81531664355656 Winsorized Mean ( 83 / 120 ) -0.736805557066667 0.453740460326642 -1.62384803977201 Winsorized Mean ( 84 / 120 ) -0.736805557066667 0.450648760187312 -1.63498853688272 Winsorized Mean ( 85 / 120 ) -0.734444445955556 0.449553718003969 -1.63371898961599 Winsorized Mean ( 86 / 120 ) -0.686666668177777 0.444164428612037 -1.54597402210603 Winsorized Mean ( 87 / 120 ) -0.679416668177778 0.443683873509523 -1.53130800721608 Winsorized Mean ( 88 / 120 ) -0.659861112622223 0.436294722359903 -1.51242056986859 Winsorized Mean ( 89 / 120 ) -0.649972223733333 0.434997783725084 -1.49419663283644 Winsorized Mean ( 90 / 120 ) -0.594972223733333 0.428468424924452 -1.38860226127104 Winsorized Mean ( 91 / 120 ) -0.544416668177778 0.424866592572405 -1.28138262149900 Winsorized Mean ( 92 / 120 ) -0.534194445955556 0.422549979284562 -1.26421600318150 Winsorized Mean ( 93 / 120 ) -0.529027779288889 0.418872586025247 -1.26298019239913 Winsorized Mean ( 94 / 120 ) -0.534250001511111 0.416170368248448 -1.28372907412805 Winsorized Mean ( 95 / 120 ) -0.600222223733333 0.410537304920705 -1.46204063927702 Winsorized Mean ( 96 / 120 ) -0.573555556 0.407458435504251 -1.40764187466188 Winsorized Mean ( 97 / 120 ) -0.616666667111111 0.404686420202919 -1.52381359078444 Winsorized Mean ( 98 / 120 ) -0.635722222666666 0.398245173381078 -1.59630866902773 Winsorized Mean ( 99 / 120 ) -0.676972222666667 0.388280228948572 -1.74351453459232 Winsorized Mean ( 100 / 120 ) -0.585305556 0.380017586594581 -1.54020649740200 Winsorized Mean ( 101 / 120 ) -0.658250000444445 0.375070736817405 -1.75500228578189 Winsorized Mean ( 102 / 120 ) -0.649750000444444 0.373822804363409 -1.73812296323366 Winsorized Mean ( 103 / 120 ) -0.658333333777777 0.372566849611932 -1.76702069565100 Winsorized Mean ( 104 / 120 ) -0.638111111555555 0.370570331020731 -1.72197032017616 Winsorized Mean ( 105 / 120 ) -0.638111111555556 0.369108178566175 -1.72879158092444 Winsorized Mean ( 106 / 120 ) -0.614555556 0.364318527496121 -1.68686330674342 Winsorized Mean ( 107 / 120 ) -0.641305556 0.362278640057108 -1.77019974431533 Winsorized Mean ( 108 / 120 ) -0.713305556 0.354455834187868 -2.01239614981746 Winsorized Mean ( 109 / 120 ) -0.598250000444445 0.346549433859355 -1.72630494236283 Winsorized Mean ( 110 / 120 ) -0.613527778222222 0.341830081849195 -1.79483261070303 Winsorized Mean ( 111 / 120 ) -0.598111111555555 0.338600419308836 -1.76642165055921 Winsorized Mean ( 112 / 120 ) -0.588777778222222 0.334200698607936 -1.76174909470474 Winsorized Mean ( 113 / 120 ) -0.566805556 0.329775595665591 -1.71876137424908 Winsorized Mean ( 114 / 120 ) -0.607972222666667 0.326085655181052 -1.86445559013966 Winsorized Mean ( 115 / 120 ) -0.623944444888889 0.324327754448249 -1.92380835846242 Winsorized Mean ( 116 / 120 ) -0.611055556 0.320000617914716 -1.90954492520028 Winsorized Mean ( 117 / 120 ) -0.698805556 0.313486202775661 -2.22914294094176 Winsorized Mean ( 118 / 120 ) -0.685694444888889 0.312286658009560 -2.19572123016507 Winsorized Mean ( 119 / 120 ) -0.718750000444444 0.308287796411395 -2.33142540447922 Winsorized Mean ( 120 / 120 ) -0.755416667111111 0.305682842846175 -2.47124326664041 Trimmed Mean ( 1 / 120 ) -0.175019245128492 0.959119157089879 -0.182479146448840 Trimmed Mean ( 2 / 120 ) -0.352004996168539 0.92284587191657 -0.381434220903534 Trimmed Mean ( 3 / 120 ) -0.490934089028249 0.895649473431896 -0.54813194624803 Trimmed Mean ( 4 / 120 ) -0.603345330670454 0.873850527832867 -0.690444545667026 Trimmed Mean ( 5 / 120 ) -0.675469843645714 0.85980818305841 -0.785605274472976 Trimmed Mean ( 6 / 120 ) -0.729544063666667 0.84862631756297 -0.859676454251058 Trimmed Mean ( 7 / 120 ) -0.78094862149133 0.837725363500071 -0.932225112808421 Trimmed Mean ( 8 / 120 ) -0.823096255569767 0.828048959728168 -0.994018826906048 Trimmed Mean ( 9 / 120 ) -0.85716959297076 0.81960871692271 -1.04582781426371 Trimmed Mean ( 10 / 120 ) -0.891996734341176 0.81104744602406 -1.0998083265214 Trimmed Mean ( 11 / 120 ) -0.921052599278106 0.803134488566339 -1.14682237208149 Trimmed Mean ( 12 / 120 ) -0.944680557845238 0.795790453007807 -1.18709712371477 Trimmed Mean ( 13 / 120 ) -0.944680557845238 0.788742066819914 -1.19770530517542 Trimmed Mean ( 14 / 120 ) -0.986796521674699 0.78154442405277 -1.26262371185194 Trimmed Mean ( 15 / 120 ) -1.00637373962424 0.774464146015314 -1.29944522906854 Trimmed Mean ( 16 / 120 ) -1.02423848462195 0.767492480984327 -1.33452575757920 Trimmed Mean ( 17 / 120 ) -1.04008316514110 0.760616892122746 -1.36742054497162 Trimmed Mean ( 18 / 120 ) -1.05683333554321 0.75361763347412 -1.40234687804648 Trimmed Mean ( 19 / 120 ) -1.06882263849689 0.747060309495054 -1.43070462305690 Trimmed Mean ( 20 / 120 ) -1.0805555577375 0.740433440543967 -1.45935542422781 Trimmed Mean ( 21 / 120 ) -1.09080084074214 0.73383403595356 -1.48644078538103 Trimmed Mean ( 22 / 120 ) -1.10127074758228 0.727017028725894 -1.51477985256036 Trimmed Mean ( 23 / 120 ) -1.10916702266242 0.720425536504124 -1.53959981491588 Trimmed Mean ( 24 / 120 ) -1.11661966024359 0.71409380424069 -1.56368764665437 Trimmed Mean ( 25 / 120 ) -1.12362007379355 0.707580161199666 -1.58797566043755 Trimmed Mean ( 26 / 120 ) -1.12362007379355 0.700960352390199 -1.60297236493066 Trimmed Mean ( 27 / 120 ) -1.13508496939869 0.694191700549412 -1.63511745890989 Trimmed Mean ( 28 / 120 ) -1.13711476814474 0.687963469142245 -1.65287085600998 Trimmed Mean ( 29 / 120 ) -1.13784694833113 0.681699797615971 -1.66913200254773 Trimmed Mean ( 30 / 120 ) -1.13878889092 0.675474890591931 -1.68590854638884 Trimmed Mean ( 31 / 120 ) -1.14239448374497 0.669342414262504 -1.70674151137379 Trimmed Mean ( 32 / 120 ) -1.14652177377027 0.663297254510381 -1.72851879903617 Trimmed Mean ( 33 / 120 ) -1.14767800651701 0.658051260760718 -1.74405563054506 Trimmed Mean ( 34 / 120 ) -1.14789117395890 0.65271298745862 -1.75864613699245 Trimmed Mean ( 35 / 120 ) -1.14869348853793 0.647316643512393 -1.77454650679925 Trimmed Mean ( 36 / 120 ) -1.147944446375 0.641947387632701 -1.78822200773845 Trimmed Mean ( 37 / 120 ) -1.14701010292308 0.636378472074091 -1.80240242757542 Trimmed Mean ( 38 / 120 ) -1.14271752928169 0.631021841661477 -1.81090012078333 Trimmed Mean ( 39 / 120 ) -1.13839952906383 0.625652380480246 -1.81953999470122 Trimmed Mean ( 40 / 120 ) -1.13226984312857 0.620425052700275 -1.82499052577035 Trimmed Mean ( 41 / 120 ) -1.12432534156835 0.61525760118213 -1.82740585310627 Trimmed Mean ( 42 / 120 ) -1.11612077476812 0.61029842426583 -1.82881149678663 Trimmed Mean ( 43 / 120 ) -1.10655555735766 0.605646172771995 -1.82706604467266 Trimmed Mean ( 44 / 120 ) -1.09747467498529 0.601004163104891 -1.82606834088395 Trimmed Mean ( 45 / 120 ) -1.08674074250370 0.596465745611016 -1.82196672734400 Trimmed Mean ( 46 / 120 ) -1.07584660207463 0.59200691411308 -1.81728722490753 Trimmed Mean ( 47 / 120 ) -1.06497660990977 0.587396063296097 -1.81304689706941 Trimmed Mean ( 48 / 120 ) -1.05432070877273 0.582641658838746 -1.80955256593577 Trimmed Mean ( 49 / 120 ) -1.05432070877273 0.57781903553734 -1.82465554772225 Trimmed Mean ( 50 / 120 ) -1.02951709567692 0.572996658882836 -1.79672443061738 Trimmed Mean ( 51 / 120 ) -1.01488889052713 0.568130496414455 -1.78636580316006 Trimmed Mean ( 52 / 120 ) -1.01488889052713 0.563249841407823 -1.80184496455508 Trimmed Mean ( 53 / 120 ) -0.988051620141732 0.558469004069562 -1.76921478710869 Trimmed Mean ( 54 / 120 ) -0.976595239666667 0.553675597260155 -1.76384013400503 Trimmed Mean ( 55 / 120 ) -0.962115557104 0.549651039689813 -1.75041160232673 Trimmed Mean ( 56 / 120 ) -0.946958782887097 0.545476102039398 -1.73602249364666 Trimmed Mean ( 57 / 120 ) -0.933018971691057 0.5413900260961 -1.72337672789975 Trimmed Mean ( 58 / 120 ) -0.919547360311475 0.53722658627765 -1.71165646637643 Trimmed Mean ( 59 / 120 ) -0.906390267752066 0.532927234504642 -1.70077678352198 Trimmed Mean ( 60 / 120 ) -0.89297222365 0.528455753360468 -1.68977670878131 Trimmed Mean ( 61 / 120 ) -0.876429506537815 0.524144706576965 -1.67211362728724 Trimmed Mean ( 62 / 120 ) -0.860072506084746 0.519709813589629 -1.65490911196045 Trimmed Mean ( 63 / 120 ) -0.860072506084746 0.515273513097281 -1.66915722276291 Trimmed Mean ( 64 / 120 ) -0.826469349982759 0.510683321479222 -1.61835978427657 Trimmed Mean ( 65 / 120 ) -0.809251209026087 0.505977354206541 -1.59938226938067 Trimmed Mean ( 66 / 120 ) -0.796730995421053 0.501774394115575 -1.58782712861498 Trimmed Mean ( 67 / 120 ) -0.783236972725664 0.497596819854998 -1.57403934565720 Trimmed Mean ( 68 / 120 ) -0.770305556767857 0.493331456441081 -1.56143612313896 Trimmed Mean ( 69 / 120 ) -0.756555556738739 0.489237379302353 -1.54639769720290 Trimmed Mean ( 70 / 120 ) -0.744601011254545 0.485214443798939 -1.53458129857958 Trimmed Mean ( 71 / 120 ) -0.733940877779817 0.481343192305459 -1.52477668638982 Trimmed Mean ( 72 / 120 ) -0.722759260351852 0.47729044511427 -1.51429652059935 Trimmed Mean ( 73 / 120 ) -0.711088266897196 0.473064351829402 -1.50315335354973 Trimmed Mean ( 74 / 120 ) -0.699857443377358 0.469115664906726 -1.49186543049359 Trimmed Mean ( 75 / 120 ) -0.686031747028571 0.465263001287966 -1.47450312001913 Trimmed Mean ( 76 / 120 ) -0.672757479596154 0.461304009199941 -1.45838203479511 Trimmed Mean ( 77 / 120 ) -0.662089537067961 0.457614443588908 -1.44682832096694 Trimmed Mean ( 78 / 120 ) -0.65155555645098 0.454003356425438 -1.43513378751416 Trimmed Mean ( 79 / 120 ) -0.646357536613861 0.451125953541323 -1.43276513253112 Trimmed Mean ( 80 / 120 ) -0.64045555638 0.448140915760818 -1.4291387683106 Trimmed Mean ( 81 / 120 ) -0.634585859373737 0.445093310141135 -1.42573668243299 Trimmed Mean ( 82 / 120 ) -0.63058616855102 0.44213832472613 -1.4262192017433 Trimmed Mean ( 83 / 120 ) -0.625782360391753 0.439205762980132 -1.42480452930683 Trimmed Mean ( 84 / 120 ) -0.62327430625 0.436556647308898 -1.42770545378727 Trimmed Mean ( 85 / 120 ) -0.620713450968421 0.433866347406135 -1.43065590285891 Trimmed Mean ( 86 / 120 ) -0.618151300893617 0.431041902869851 -1.43408633076739 Trimmed Mean ( 87 / 120 ) -0.616609319634409 0.428270857123374 -1.43976483428285 Trimmed Mean ( 88 / 120 ) -0.615196860521739 0.425329434357518 -1.44640086207771 Trimmed Mean ( 89 / 120 ) -0.614192918791209 0.422526498931056 -1.45361988027981 Trimmed Mean ( 90 / 120 ) -0.613388889466667 0.41958521593165 -1.46189347521383 Trimmed Mean ( 91 / 120 ) -0.613802747123596 0.416742555198192 -1.47285833776127 Trimmed Mean ( 92 / 120 ) -0.615362374272727 0.413863964951011 -1.48687111318224 Trimmed Mean ( 93 / 120 ) -0.617187739977011 0.410885318659132 -1.50209246217684 Trimmed Mean ( 94 / 120 ) -0.619171835116279 0.407865535368850 -1.51807834058923 Trimmed Mean ( 95 / 120 ) -0.621084967788235 0.404753643705502 -1.53447653269339 Trimmed Mean ( 96 / 120 ) -0.621555556 0.401689607680064 -1.54735284188645 Trimmed Mean ( 97 / 120 ) -0.622639893349398 0.398546208277207 -1.56227779970829 Trimmed Mean ( 98 / 120 ) -0.622639893349398 0.395302449383711 -1.57509748376240 Trimmed Mean ( 99 / 120 ) -0.622481481925926 0.392139503391394 -1.58739804723175 Trimmed Mean ( 100 / 120 ) -0.621243056 0.389242455098642 -1.59603108001814 Trimmed Mean ( 101 / 120 ) -0.622061885113924 0.386538061466049 -1.60931599531127 Trimmed Mean ( 102 / 120 ) -0.621235043179487 0.383865298738306 -1.61836728983154 Trimmed Mean ( 103 / 120 ) -0.620581530025974 0.381031560695428 -1.62868799868793 Trimmed Mean ( 104 / 120 ) -0.620581530025974 0.378023957465234 -1.64164603266725 Trimmed Mean ( 105 / 120 ) -0.619288889333333 0.374869166100343 -1.65201340984008 Trimmed Mean ( 106 / 120 ) -0.618852853297297 0.371524707816399 -1.66571116342315 Trimmed Mean ( 107 / 120 ) -0.618952816273973 0.368164901835762 -1.6811836576157 Trimmed Mean ( 108 / 120 ) -0.618430556 0.364628440016867 -1.69605682971793 Trimmed Mean ( 109 / 120 ) -0.618430556 0.361240021082387 -1.71196578426441 Trimmed Mean ( 110 / 120 ) -0.616626984571429 0.358018563546746 -1.72233243567806 Trimmed Mean ( 111 / 120 ) -0.616700483536232 0.354783264945283 -1.73824569665467 Trimmed Mean ( 112 / 120 ) -0.617143791294118 0.35144178239492 -1.75603420597448 Trimmed Mean ( 113 / 120 ) -0.617824212716418 0.348057592773596 -1.77506316639470 Trimmed Mean ( 114 / 120 ) -0.619055556 0.344628192356518 -1.79629980869234 Trimmed Mean ( 115 / 120 ) -0.619055556 0.341103356602257 -1.81486210562815 Trimmed Mean ( 116 / 120 ) -0.619211806 0.337345774115623 -1.83554042620901 Trimmed Mean ( 117 / 120 ) -0.619412698857143 0.333507356614663 -1.85726847270964 Trimmed Mean ( 118 / 120 ) -0.617442652774194 0.32973001958112 -1.87257033362803 Trimmed Mean ( 119 / 120 ) -0.615735883868852 0.32564714347501 -1.89080695533908 Trimmed Mean ( 120 / 120 ) -0.613138889333333 0.321428272551474 -1.90754498497062 Median -0.766555556 Midrange 30.71844444 Midmean - Weighted Average at Xnp -0.67022958930387 Midmean - Weighted Average at X(n+1)p -0.613388889466669 Midmean - Empirical Distribution Function -0.67022958930387 Midmean - Empirical Distribution Function - Averaging -0.613388889466669 Midmean - Empirical Distribution Function - Interpolation -0.613388889466669 Midmean - Closest Observation -0.67022958930387 Midmean - True Basic - Statistics Graphics Toolkit -0.613388889466669 Midmean - MS Excel (old versions) -0.614192918791211 Number of observations 360

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053909umgj0hx3hm0rzgo/1v47t1256053835.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053909umgj0hx3hm0rzgo/1v47t1256053835.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053909umgj0hx3hm0rzgo/24qx91256053835.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053909umgj0hx3hm0rzgo/24qx91256053835.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file='test2.png') lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Measure',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'Value/S.E.',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste('Winsorized Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste('Trimmed Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number of observations',header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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